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2 years ago

PLEASE HELP!!

Mathematics

1 answer:

jonny [76]2 years ago

7 0

Answer:

A. f(n) = (n + 1)^2 – 1

Step-by-step explanation:

Figure 1

3 = 4 - 1 = 2² - 1 = (1 + 1)² - 1

Figure 2

8 = 9 - 1 = 3² - 1 = (2 + 1)² - 1

Figure 3

15 = 16 - 1 = 4² - 1 = (3 + 1)² - 1

The function is:

f(n) = (n + 1)² - 1

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Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

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Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

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Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

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